PolySketchFormer: Fast Transformers via Sketching Polynomial Kernels
This addresses a critical efficiency problem for training and deploying large-scale language models, offering a practical solution with provable guarantees, though it builds incrementally on existing polynomial and sketching methods.
The paper tackles the quadratic computational bottleneck of self-attention in Transformers by replacing softmax with polynomial attention and using sketching techniques to achieve linear-time complexity, resulting in a 2.5-4x training speedup for long-context models without quality degradation.
The quadratic time and memory complexity inherent to self-attention mechanisms, with respect to sequence length, presents a critical computational bottleneck in the training and deployment of large-scale Transformer-based language models. Recent theoretical results indicate the intractability of sub-quadratic softmax attention approximation under reasonable complexity assumptions. This paper addresses this challenge by first demonstrating that polynomial attention with high degree can effectively replace softmax without sacrificing model quality. Next, we develop polynomial sketching techniques from numerical linear algebra to achieve linear-time polynomial attention with approximation guarantees. Crucially, our approach achieves this speedup without requiring the sparsification of attention matrices. We also present a block-based algorithm to apply causal masking efficiently. Combining these techniques, we provide \emph{PolySketchFormer}, a practical linear-time Transformer architecture for language modeling that offers provable guarantees. We validate PolySketchFormer empirically by training language models capable of handling long contexts. These experiments utilize both synthetic and real-world datasets (PG19, Wikipedia and C4) on Google Cloud TPUs. For context lengths of 32k and GPT-2 style models, our model achieves a 2.5-4x speedup in training compared to FlashAttention, with no observed degradation in quality across our experiments.